S000767


Primes p for which the polynomial (x^29 - 1)/(x - 1) mod p is irreducible.

2, 3, 11, 19, 29, 31, 37, 43, 47, 61, 73, 79, 89, 97, 101, 113, 127, 131, 137, 163, 193, 211, 229, 251, 263, 269, 271, 293, 311, 317, 337, 359, 367, 379, 409, 421, 433, 443, 449, 461, 467, 479, 491, 503, 541, 569, 577, 599, 601, 607, 617, 619, 641, 653, 659

1

S000767

This is the 28nd-degree cyclotomic polynomial. These primes p satisfy the congruence p mod 29 == {0, 2, 3, 8, 10, 11, 14, 15, 18, 19, 21, 26, 27}.  The fraction of all primes in this sequence is 3/7. If we plotted n versus primepi(s(n)), then the plotted points would be very close to the line having slope 7/3.

T. D. Noe, Plot of 1000 terms

T. D. Noe, Table of 1000 terms

Wikipedia, Cyclotomic polynomial

(Mma) t = {}; n = 29; p = 1; While[Length[t] < 100, p = NextPrime[p]; If[Length[FactorList[(x^n - 1)/(x - 1), Modulus -> p]] == 2, AppendTo[t, p]]]; t

Cf. A045309A042993A045401S000762-S000782.

nonn

T. D. Noe, Dec 01 2015

© Tony D Noe 2014-2015